In this paper, we perform direct numerical simulations (DNS) of turbulent boundary layers with nominal free-stream Mach number ranging from 0.3 to 12. The main objective is to assess the scaling's with respect to the mean and turbulence behaviors as well as the possible breakdown of the weak compressibility hypothesis for turbulent boundary layers at high Mach numbers (M > 5). We find that many of the scaling relations, such as the van Driest transformation for mean velocity, Walz's relation, Morkovin's scaling and the strong Reynolds analogy, which are derived based on the weak compressibility hypothesis, remain valid for the range of free-stream Mach numbers considered. The explicit dilatation terms such as pressure dilatation and dilatational dissipation remain small for the present Mach number range, and the pressure-strain correlation and the anisotropy of the Reynolds stress tensor are insensitive to the free-stream Mach number. The possible effects of intrinsic compressibility are reflected by the increase in the fluctuations of thermodynamic quantities (p′rms/pw, ρ′rms/ρ, T′rms/T) and turbulence Mach numbers (Mt, M′rms), the existence of shocklets, the modification of turbulence structures (near-wall streaks and large-scale motions) and the variation in the onset of intermittency.
L. Duan et al., "Direct Numerical Simulation Of Hypersonic Turbulent Boundary Layers. Part 3. Effect Of Mach Number," Journal of Fluid Mechanics, vol. 672, pp. 245 - 267, Cambridge University Press, Apr 2011.
The definitive version is available at https://doi.org/10.1017/S0022112010005902
Mechanical and Aerospace Engineering
Keywords and Phrases
compressible turbulence; high-speed flow; turbulent boundary layers
International Standard Serial Number (ISSN)
Article - Journal
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10 Apr 2011